I'm just not sure why you want to do this. My pool overfills when it rains and only needs water when there's no rain.
In the hot sunny summer I get about an inch of water loss a week from evaporation. I don't bother to refill the pool with a hose until it is at least an inch below the drain. If it is an inch below the drain, in a long heavy rain my pool will over fill, but a lighter or shorter rain might only fill it half an inch. I thought if I ran something from the down spout it might be better.